Are there any ways to estimate melting points?

Are there any ways to estimate melting points?

Are there any ways to estimate melting points? What do melting points measure? Melting is a function of the detailed structure of the crystalline state, and that diverse laws of melting must be looked for because of the diversity of the crystal structure -Alfred Ubbelohde, Melting and Crystal Structure 1965. 450 400 350 Tf(exp)/ K 300 250 200 150 100 50 0 100 200 300 400 500 number of methylene groups, n Figure . Melting temperatures of the even n-alkanes versus the number of methylene groups, circles; experimental data 400 Experimental melting point, K 350 300 250 200 150 100 50 0

10 20 30 40 50 60 70 80 Number of methylene groups, n Figure. Melting points of the odd alkanes versus the number of methylene groups; circles: experimental data 80 70 80 60 70 60 40 30 20 50 1/[1-Tf (n)/Tf ( 1/[1-Tf (n)/Tf ( 50 10 40 30 20 0 10 0 0

100 200 300 400 500 number of methylene groups, n 0 100 200 300 number of methylene groups, n 400 500 Figure. The correlation between the function 1/[1-Tf (n)/Tf ()] and the 14 12 1/(1-mp(n)/mp ) 10 8 6 4 2 0 0 10 20 30 40 50

60 70 80 Number of methylene groups, n Figure. The correlation between the function 1/[1-Tf (n)/Tf ()] and the number of methylene groups for the odd n-alkanes. 450 400 350 Tf / K 300 250 1-alkenes n-alkylbenzenes carboxylic acids N-(2-hydroxyethyl)alkanamides 1,-dicarboxylic acids calculated 200 150 100 50 0 5 10 15 20 25 30 35 40 number of methylene groups, n Figure. Melting temperatures of the odd 1-alkenes, n-alkylbenzenes, n-carboxylic acids, N-(2-hydroxyethyl)alkanamides and 1,-dicarboxylic acids versus the number of methylene groups, circles, squares triangles and hexagons: experimental data; lines: calculated results. Conclusions drawn from the n-alkane results:

The melting point of an alkane is not a group property. 2. The odd and even members of the series should be segregated. 3. The melting point of any long chain approaches the melting point of polyethylene. Since the nature of what is attached to the end of the polyethylene is not crucial to the properties of the polymer produced, we surmised that the mp behavior observed in n-alkanes should apply to any homologous series. 4. The first few members of the series usually deviate from the observed hyperbolic behavior. Tfus = Tf ()*[1- 1/(mn + b)] Table. Melting-structure correlations of series related to polyethylene: parents with Tf <411.3 K.a Homologous Series Parent Compound Tf /K S m b r2 /K nT Parent A. Hydrocarbons n-alkanesb 1-alkenesc 2-methylalkanesc 3-methylalkanesc 4-methylalkanesc 5-methylalkanese butane 134.9 e 0.161

1.153 0.989 2.0 53 propane 85.2 o 0.172 0.948 0.994 3.5 24 1-pentene 107.9 e 0.170 0.856 0.999 7.2 9 1-butene 87.8 o 0.164 0.925 0.998 2.4 8 2-methylpentane 119.6

e 0.155 0.951 0.993 5.5 10 2-methylbutane 113.4 o 0.144 1.18 0.998 2.1 9 3-methylhexane 100.2 e 0.145 0.981 0.984 4.8 6 3-methylheptane 152.7 o 0.129 1.19 0.996 2.4 7 4-methylheptane 152.2

e 0.125 1.29 0.998 1.5 6 4-methyldecaned 195.7 o 0.128 1.23 0.995 2.1 7 5-methyldecaned 183.2 e 0.121 1.24 0.995 1.9 7 5-methylnonane 186.7 o 0.113 1.41 0.996 2.0 6 2,3-dimethylalkanesc 2,3-dimethyldecaned 183.7 e 0.155

2,3-dimethylheptane 156 o 0.15 e 0.136 1.13 0.992 2.6 5 o 0.128 1.16 0.997 2.0 6 2,4,6-trimethylalkanese 2,4,6-trimethyltridecaned 171.2 e 0.151 0.781 0.962 7.5 4 2,4,6-trimethyldodecaned 161.2 o 0.114 1.04 0.957 7.8 4

2,4-dimethylalkanesc 2,4-dimethylundecaned 197.7 2,4-dimethyldecaned n-alkylcyclopentanesf propylcyclopentane n-alkylcyclohexanesf n-alkylbenzenesc 1-alkylnaphthalenesg 2-alkylnaphthalenesg Alkynesf 183.2 0.898 0.884 0.989 0.991 4.0 7.4 5 6 155.8 e 0.155 1.23 0.999 0.6 8 ethylcyclopentane 134.7 o 0.155 1.17 0.999 1.6 8 propylcyclohexane 178.3

e 0.165 1.45 0.999 0.6 7 ethylcyclohexane 161.4 o 0.164 1.47 0.999 4.1 9 propylbenzene 173.6 e 0.166 1.21 0.999 1.4 8 ethylbenzene 178 o 0.164 1.23 0.999 3.4

10 1-propylnaphthalene 263.2 e 0.190 1.67 0.997 1.4 4 1-ethylnaphthalene 259.3 o 0.171 1.77 0.998 6.7 6 2-propylnaphthalene 270.2 e 0.131 2.29 0.955 3.5 5 2-ethylnaphthalene 265.7 o 0.149 2.15 0.987

6.8 6 1-pentyne 167.5 e 0.172 1.15 0.999 0.7 9 1-butyne 147.5 o 0.180 0.993 0.999 2.0 9 B. Cycloalkanes Cycloalkanesh m b 0.188 1.18 r2 0.856 /K nT

21 46 420 400 380 Tf / K 360 experimental data calculated 340 320 300 280 0 50 100 150 200 250 300 350 Number of methylene groups, n Figure. Melting temperatures of the cycloalkanes versus the number of methylene groups. Both even and odd members are included. C. Functionalized Alkanes Homologous Series Parent Compound Tf /K 1-alkanolsi S m

b r2 /K nT propanol 147.2 e 0.239 0.968 0.998 1.9 18 ethanol 143.2 o 0.244 0.953 0.999 4.0 15 2-nonanold 184.7 e 0.257 0.87 0.992 3.1 6 2-butanol

158.5 o 0.244 1.22 0.999 1.1 9 1-alkanethiolsc 1-ethanethiol 125.9 o 0.153 1.12 0.998 2.6 8 2-alkanolsj methyl alkanoatesk methyl hexanoate 202.2 e 0.179 1.30 0.995 2.6 17 methyl propanoate 185.2 o 0.167 1.26

0.991 4.1 11 propyl ethanoate 178.2 e 0.161 1.22 0.999 3.1 8 ethyl ethanoate 189.6 o 0.155 1.28 0.999 7.2 9 172.4 e 0.166 1.28 0.999 1.4 18 alkyl ethanoatesc ethyl alkanoatesi ethyl butanoate

n-alkanalc butanal 176.8 e 0.159 1.77 0.982 7.4 propanal 193.2 o 0.183 1.24 0.945 8.1 268.5 e 0.270 1.72 0.998 1.2 propanoic acid 253.5 o 0.265 1.44 0.999 1.0

15 1-chloropropane 150.2 e 0.160 1.07 0.997 2.4 8 chloroethane 137.2 o 0.166 0.941 0.999 6.5 9 1-fluorotridecaned 276.2 e 0.183 0.839 0.999 0.3 4 1-fluoroethane 130 o 0.171 0.846

0.999 7.3 9 1-bromopropane 163.2 e 0.164 1.15 0.999 0.9 9 bromoethane 154.6 o 0.159 1.04 0.999 4.9 11 1-iodopropane 171.9 e 0.172 1.21 0.999 2.4 18 iodoethane

162.1 o 0.168 1.10 0.999 3.0 19 1-cyanopropane 161.3 e 0.203 1.03 0.999 1.1 8 cyanoethane 180.3 o 0.191 1.09 0.998 2.9 9 1,2-dihydroxyalkanesc 1,2-hexanediol 318.2 o 0.336 2.18 0.995 5.2

7 n-alkanoic acidsj butanoic acid 18 1-chloroalkanesc 1-fluoroalkanesc 1-bromoalkanesf 1-iodoalkanes f 1-cyanoalkanesc 1-N-methylamino-alkanesc 7 8 1-N,N-dimethyl-aminoalkanesc dimethyl-n-ethylamine 2-alkanonesc 133.2 o 0.165 0.774 0.999 0.3 7 2-pentanone 195.2 e 0.220 1.51 0.999 0.7 7 2-butanone

186.2 o 0.220 1.51 0.999 1.9 8 293.2 o 0.213 2.44 0.995 0.8 5 alkyl phenyl ketonesk acetophenone F-[CF2]12-[CH2]n-Hh F-[CF2]12-[CH2]2-H 344.2 e 0.172 5.93 0.920 1.5 9 N-methyl alkanamidesl N-methylbutanamide 268 e 0.461 1.37 0.999

0.8 7 N-methylpropanamide 230.2 o 0.435 1.13 0.999 0.6 7 319.2 e 0.435 2.93 0.967 2.1 6 N-(2-hydroxyethyl)pentanamided 305.2 o 0.639 1.71 0.993 1.4 5 p-chlorophenacyl butanoate 328.2 e 0.288 3.27 0.953

6.0 6 p-chlorophenacyl propionate 371.4 o 0.231 4.05 0.809 8.8 7 e 0.257 5.49 0.981 1.3 7 2-hydroxyethyl- alkanamidesl N-(2-hydroxyethyl)hexanamide p-chlorophenacyl alkanoatesl N-octadecyl alkanamidesm N-octadecyl butanamide 349.7 n-alkanamidesn butanamide propanamide 389.2 356.2 e o 0.226 0.238 9.93 8.61

0.706 0.732 3.5 5.0 12 7 propyl 4-nitrobenzoate 308.2 e 0.162 2.22 0.995 3.0 7 ethyl 4-nitrobenzoate 330.2 o 0.213 1.94 0.984 6.9 9 367.2 o 0.035 5.13 0.566 2.7 8 1,2-dihydroxyethane

260.2 e 0.421 1.87 0.988 1.9 8 1,3-dihydroxypropane 246.2 o 0.476 0.25 0.993 8.1 6 N-(-naphthyl) hexanamide 380.2 e 0.400 9.07 0.970 1.2 6 N-(-naphthyl) pentanamide 385.2 o 0.356 9.28 0.998 3.2 3

o 0.730 9.30 0.925 1.9 8 alkyl 4-nitrobenzoateso n-alkyl 3,5-dinitrobenzoateso ethyl 3,5-dinitrobenzoate 1, dihydroxyalkanesc N-(-naphthyl)alkanamidesm 1,-alkanedioic acidsk 1,5-undecanedioic acidd 378 D. Symmetrically Substituted Derivativesq sym dialkyl etherc,p diethyl ether 157.2 e 0.135 0.932 0.999 1.7 4 butanoic anhydride 198.2 e 0.319 1.05 0.999

1.4 10 propanoic anhydride 228.2 o 0.221 2.25 0.980 23.8 5 o 0.292 1.01 0.998 1.4 6 0.298 1.14 0.913 10.2 8 210.2 o 0.320 1.08 0.999 0.9 8 158.5 o 0.249 0.655 0.998 1.6

7 sym n-alkanoic acid anhydridesp,q sym di-n-alkyl sulfidesr diethyl sulfide 171.2 sym N,N-dialkylaminesc diethylamine dipropylamine 181 e sym-tri-n-alkylaminesc triethylamine sym-1,2,3-glycerol tri-alkanoates form 304.8 form ' form e 0.296 1.50 0.999 0.5 7 261.7 0.272 0.598 0.999 1.1 7 290.0 0.263

1.31 0.999 0.8 7 380 360 340 Tf / K 320 300 calculated value form ' form form 280 260 240 6 8 10 12 14 16 Number of methylene groups, n 18 20 22 Figure. Experimental melting points of the three polymorphic forms of symmetric glycerol trialkanoates ranging from decanoate to eicosanoate. Molecular packing in each series series is very similar. If homologous series related to polethylene converge to the mp of polyethylene, what about other series converging to other polymers?

500 450 400 Tf / K 350 300 250 Tf ; n = number of CF2 200 Tf ; n = number of -(CH2CH2O)Tf ; n = number of -(NH(CH2)5CO)calculated 150 100 0 10 20 30 40 50 number of repeat units, n Figure. Experimental melting points as a function of the number of repeat units, circles: perfluoro-n-alkanes; squares: H[OCH 2CH2]nOH; triangles: C2H5CO-[NH(CH2)5CO]n-NHC3H7. 5 1/(1 - mp(n)/mp 4 3 2 1 0 0 5 10 15

20 25 Number of CF2 groups, n Figure. A plot of 1/(1 mp(n)/mp) versus the number of CF2 groups. The melting point of Teflon is 605 K. Table. Melting-structure correlations of series related to other polymers Parent Compound Tf /K n-perfluoroalkanes perfluorobutane perfluoropropane 14.3 4 Polyethers S m b r2 /K nT 6 Teflon (Tf 605 K) 164 e 0.159 125.5 o 0.768 0.999 1.3 0.140

0.855 0.920 Polyoxyethylene (Tf 342 K) H[OCH2CH2]2OH 267.2 e 0.407 3.36 0.884 4.7 8 H[OCH2CH2]OH 260.6 o 0.554 2.34 0.953 5.2 8 0.650 0.8 5 Polyamides Nylon-6 (Tf 533 K) H[NH(CH2)5CO]2OH 471.2 e 0.089 10.0 What if the melting temperature of the parent is greater than 411 K? 560 4-n-alkoxy-3-fluorobenzoic acid trans 4'-n-alkoxy-3-chlorocinnamic acid 6-n-alkoxy-2-naphthoic acid

8-n-alkyltheophylline calculated 540 520 Tf or Ttr / K 500 480 460 440 420 400 380 360 0 2 4 6 8 10 12 number of methylene groups, n 14 16 18 Figure 6. Experimental melting or smetic/nematic isotropic transition temperatures for the odd series of 4alkoxy-3-fluorobenzoic acids, trans-4-n-alkoxy-3-chlorocinnamic acids, 6-alkoxy-2-naphthoic acids, and the even series of 8-alkyltheophyllines; symbols: experimental data; lines: calculated results. Figure. Melting temperatures of the dialkylarsinic acids (odd series) 420 M elting tem perature / K 415 410 405 400 395 390

0 2 4 6 8 10 12 Number of methylene groups 14 16 18 35 [1/(1- Tn)] 30 25 20 15 10 0 2 4 6 8 10 12 14 16 18 Number of repeat units

Figure. A plot of [1/(1- T/T(n)] vs n for the dialkylarsinic acids. A value of 380 K was used for T. Ascending hyperbola Tfus = Tf ()*[1- 1/(mn + b)] Descending hyperbola Tfus = Tf ()/[1- 1/(mn + b)] Some of the compounds that show descending behavior relative to the parent show liquid crystalline behavior. For these compounds, which temperature correlates with the melting temperature of members of the series that do not form liquid crystals? Liquid Crystals nematic 500 N um ber of repeat units 480 460 440 420 400 380 0 2 4 6 8 10 12 14 16 18 Transition temperatures Figure. Circles: melting temperatures or temperatures at which the trans-4-n-alkoxy-3chlorocinnamic acids becomes isotropic; squares are melting temperatures for compounds

forming liquid crystals; triangles: smectic to nematic transitions 50 melting temperature nematic to isotropic smectic to nematic solid to smectic calculated 1/[1-380/T(n)] 40 30 20 10 0 0 2 4 6 8 10 12 14 16 18 number of methylene groups, n Figure. A plot of 1/[1-T()/T(n)] versus the number of methylene groups for trans-4-n-alkoxy-3chlorocinnamic acids. The solid circles represent melting temperatures, the solid squares represent nematic to isotropic transitions, the circles represent smectic to nematic transitions and the squares represent from nematic to isotropic transitions. The temperatures at which the liquids become isotropic appear to correlate best. A value of 380 K was used for T(). Why do the first few members of the series usually deviate from the observed hyperbolic behavior? Why do homologous series exhibit melting points that behave in a hyperbolic fashion? Total phase change enthalpy, kJ mol-1 8e+5 7e+5

6e+5 5e+5 4e+5 3e+5 2e+5 1e+5 0e+0 0 50 100 Number of methylene groups, n Figure. Total phase change enthalpies of the n-alkanes. 150 200 Total phase change entropy, J mol-1 K-1 2000 1800 1600 1400 1200 1000 800 600 400 200 0 0 50 100 150 Number of methylene groups, n Figure. Total phase change entropies of the n-alkanes 200 140 Total phase change enthalpy/ kJ mol -1 120 100

80 60 40 20 0 0 2 4 6 8 10 12 14 16 18 20 Number of alkyl groups on a chain Figure. Total phase change enthalpies of the dialkyl arsenic acids as a function of the size of the alkyl group. 350 -1 Total phase change entropy/ J mol K -1 300 250 200 150 100 50 0

0 2 4 6 8 10 12 14 16 18 20 Number of methylene groups per alkyl chain Figure. Total phase change entropies of the dialkyl arsenic acids as a function of the size of the alkyl group. Fusion Enthalpies N- Alkanes tpceH(Tf)/J.mol-1 = (372538)n - (18387500); (37 data points) r2 = 0.9964 Di-n-alkylarsinic acids tpceH(Tf)/J.mol-1 = 2 (334866) n + (95122800); (17 data points) r2 = 0.9941 Total Phase Change Entropies (Fusion Entropies) tpceS(Tf ) = (As)n + (Bs) J.mol-1.K-1 N-Alkanes tpceS(Tf ) = (9.3)n + (35.2) J.mol-1. K-1; Di-n-alkylarsinic Acids tpceS(Tf ) = 2(9.3)n + (11.2) J.mol-1. K-1; G = H - Tf S ; at Tf , : G = 0 Tf = tpceH/tpceS = (AHn + BH)/(ASn + BS); N-Alkanes Tf = tpceH(Tf) tpceS(Tf ) = (3725)n - (1838) (9.3)n + (35.2)

Di-n-alkylarsinic Acids Tf = tpceH(Tf) tpceS(Tf ) = 2 (3348)n+ (9512) 2(9.3)n + (11.2) 500 450 400 350 Tf / K 300 250 even n-alkanes dialkylarsinic acids 200 150 100 50 0 20 40 60 80 100 120 140 160 180 n, even number of methylene groups Figure. The melting point behavior of the even n-alkanes and the dialkylarsinic acids of formula [CH3(CH2)n]2AsOH when calculated as a ratio of the total phase change enthalpy to the total phase change entropy. Both were estimated by group additivity. 300 250 Number of entries 200 150

100 50 0 -60 -40 -20 0 20 40 60 Tf (exp) - Tf (calcd) /K Figure. The distribution of errors based on the use of three experimental data points to estimate the melting behavior of each series for 995 compounds.

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